Problem: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 6x - 6$ and $ JT = 7x - 8$ Find $CT$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {6x - 6} = {7x - 8}$ Solve for $x$ $ -x = -2$ $ x = 2$ Substitute $2$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 6({2}) - 6$ $ JT = 7({2}) - 8$ $ CJ = 12 - 6$ $ JT = 14 - 8$ $ CJ = 6$ $ JT = 6$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {6} + {6}$ $ CT = 12$